Analysis of a Finite State Many Player Game Using Its Master Equation
36 Pages Posted: 18 Jul 2017 Last revised: 20 Jul 2018
Date Written: July 9, 2017
We consider an n-player symmetric stochastic game with weak interaction between the players. Time is continuous and the horizon and the number of states are finite. We show that the value function of each of the players can be approximated by the solution of a partial differential equation called the master equation. Moreover, we analyze the fluctuations of the empirical measure of the states of the players in the game and show that it is governed by a solution to a stochastic differential equation. Finally, we prove the regularity of the master equation, which is required for the above results.
Keywords: Game theory, Mean-field games, master equation, fluctuations, finite state control problem, Markov chains
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